SOLUTION: What do I solve this by factoring? 49x^2 - 14x

SOLUTION: What do I solve this by factoring? 49x^2 - 14x - 3 Thanks!

Question 139520: What do I solve this by factoring?
49x^2 - 14x - 3
Thanks!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 49 and -3 respectively.

Now multiply the first coefficient 49 and the last coefficient -3 to get -147. Now what two numbers multiply to -147 and add to the middle coefficient -14? Let's list all of the factors of -147:

Factors of -147:
1,3,7,21,49,147

-1,-3,-7,-21,-49,-147 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -147
(1)*(-147)
(3)*(-49)
(7)*(-21)
(-1)*(147)
(-3)*(49)
(-7)*(21)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to -14? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -14

First Number	Second Number	Sum
1	-147	1+(-147)=-146
3	-49	3+(-49)=-46
7	-21	7+(-21)=-14
-1	147	-1+147=146
-3	49	-3+49=46
-7	21	-7+21=14

From this list we can see that 7 and -21 add up to -14 and multiply to -147

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

Set the factorization equal to zero

Now set each factor equal to zero:
or

or Now solve for x in each case

-------------------------
Answer:

So our solutions are

or

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